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Proof step 79 from proof validrefs-putshort-field (previous step)

refs1 .first = (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval, st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, refs1, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_referencevalue(st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), r0 ≠ r ∨ class0 ≠ class ∨ ty0 ≠ short_type ∨ fieldvar0 ≠ fieldvar, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs1, ty, st), junkref(str, r0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 78:
(st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']) = refval(r1), refs1 .first = r1, st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, refs1, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_referencevalue(st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- mkfs(class0, ty0, fieldvar0) ']), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), r0 ≠ r ∨ class0 ≠ class ∨ ty0 ≠ short_type ∨ fieldvar0 ≠ fieldvar, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs1, ty, st), junkref(str, r0, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)] [r0 -- mkfs(class0, ty0, fieldvar0) ' ], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)] [r0 -- mkfs(class0, ty0, fieldvar0) ' ], r1)]]